For the contents on display -- the National Gallery of Art, Washington, DC, hands down. Neither the Met in NYC nor the MFA in Boston can come close to competing with the treasures at the National Gallery. For quirky architecture, definitely the Guggenheim, NYC. I'm intimately familiar with the MFA, having worked there as a gallery guard several years ago, but -- frankly -- the Isabella Stewart Gardner impresses me more. Let's hope that when the East Wing addition to the MFA is completed, they'll be able to display more of the stuff they have to keep in storage. They have one of the largest collections of Impressionist work in the world and the third most valuable Egyptology collection in the world (only Cairo and London have more imppressive collections; the Met's, by comparison, is original amateur hour).
For science museums, I'm trying to remember whether I've ever actually visited the Boston Museum of Science. Maybe as a kid years and years ago. The New York Museum of Natural History is quite impressive, but I still prefer the Smithsonian in D.C. I know, I know. It's spread out over too many venues, but if you've got the time, that's the place to go.
Have to mention the Museum of Asian Art in San Francisco. Comprehensive and extremely well laid out. And the SF Museum of Modern Art compares quite favorably with MoMa in NYC.
The Chicago Art Institute is a nice big, rambling building. But it contains hardly anything I'd consider memorable.